'I ate the product and we knew straight away something was wrong,' he told 9 News.
Within half an hour, he was inside the emergency department at St Vincent's Hospital being injected with adrenalin.
A week later, Burgess relapsed and spent the next month covered in eczema, his eyes red and swollen, his face puffy.
The dessert, made by brand Sweet Bondi, contained undeclared milk and the product was recalled and stripped from shelves.
According to 9 News, the number of food recalls due to undeclared allergens is growing at an alarming rate in Australia.
In the past decade, undeclared dairy accounted for almost a third of such recalls. Peanut was the next most common undeclared allergen.
So far this year, three in every four undeclared allergen recalls were for products made in Australia.
Food Standards Australia New Zealand spokesman Lorraine Haase said, 'This is a worrying trend and seems to be increasing.'
'The message for business is really clear - this is about life and death. Allergies can be life threatening so its vitally important that food businesses get their mandatory allergen labelling requirements right.'
Maria Said, CEO of Allergy and Anaphylaxis Australia, said undeclared allergens are a 'huge problem' in Australia.
'At worst even a sip of a drink with undeclared milk or a bite of biscuit with undeclared peanut or tree nut or egg can cause death,' she said.